Don't worry, I have a really easy approach for you. Using this, your double integrals will become funny and nonsense, instead of troubling you.

Ok, forget everything, clear your mind, have fresh air..

Now, we have a double integral over a region, which is shown as . You probably already know that can be or , depending on your solution.

Your region is a triangle, which is not a rectangle. Integrals on rectangular regions can be expressed as or where a b c d are constant and limits of the rectangle.

Since your region is not a rectangle, your integral can't be expressed using only constants like a b c d. We need functions here.

In order to use my approach, the region has to be bounded by two lines parallel to one of the axes. For example, if a region is bounded by "x=a and x=b" or "y=a and y=b", then we can go on. If it's not bounded, you should split the region. You may also need to split the region if the bottom and top functions are piecewise.

When we use and as bounds, the top and bottom functions are top and bottom bounds of the region. Also dA = dy dx. If the bottom bound is and top bound is , our integral is:

When we use and as bounds, the top and bottom functions are left and right bounds of the region. Also dA = dx dy. If the bottom bound is and top bound is , our integral is:

Don't worry, I have a really easy approach for you. Using this, your double integrals will become funny and nonsense, instead of troubling you.

Ok, forget everything, clear your mind, have fresh air..

Now, we have a double integral over a region, which is shown as . You probably already know that can be or , depending on your solution.

Your region is a triangle, which is not a rectangle. Integrals on rectangular regions can be expressed as or where a b c d are constant and limits of the rectangle.

Since your region is not a rectangle, your integral can't be expressed using only constants like a b c d. We need functions here.

In order to use my approach, the region has to be bounded by two lines parallel to one of the axes. For example, if a region is bounded by "x=a and x=b" or "y=a and y=b", then we can go on. If it's not bounded, you should split the region. You may also need to split the region if the bottom and top functions are piecewise.

When we use and as bounds, the top and bottom functions are top and bottom bounds of the region. Also dA = dy dx. If the bottom bound is and top bound is , our integral is:

When we use and as bounds, the top and bottom functions are left and right bounds of the region. Also dA = dx dy. If the bottom bound is and top bound is , our integral is:

"When we use and as bounds, the top and bottom functions are top and bottom bounds of the region. Also dA = dy dx."

I think that's where I went wrong! This was crystal clear and I appreciate it so much. I've been struggling a lot in this class for the past 2 weeks and the math tutors at school seriously make no sense. They're geniuses but all I hear coming out of their mouths are infinite this and that...

Thanks for the picture and spending your time to explain this stuff to me. The explanation of the bounds was very good and I understand it much better now.

Don't worry, I have a really easy approach for you. Using this, your double integrals will become funny and nonsense, instead of troubling you.

Ok, forget everything, clear your mind, have fresh air..

Now, we have a double integral over a region, which is shown as . You probably already know that can be or , depending on your solution.

Your region is a triangle, which is not a rectangle. Integrals on rectangular regions can be expressed as or where a b c d are constant and limits of the rectangle.

Since your region is not a rectangle, your integral can't be expressed using only constants like a b c d. We need functions here.

In order to use my approach, the region has to be bounded by two lines parallel to one of the axes. For example, if a region is bounded by "x=a and x=b" or "y=a and y=b", then we can go on. If it's not bounded, you should split the region. You may also need to split the region if the bottom and top functions are piecewise.

When we use and as bounds, the top and bottom functions are top and bottom bounds of the region. Also dA = dy dx. If the bottom bound is and top bound is , our integral is:

When we use and as bounds, the top and bottom functions are left and right bounds of the region. Also dA = dx dy. If the bottom bound is and top bound is , our integral is: